problem([]==>x:pnat=>y:pnat=>times(x,y)=0 in pnat=>x=0 in pnat\y=0 in pnat,
ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(elementary(intro(new[y])then[intro(new[v0])then[intro(left)then[identity,wfftacs],wfftacs],wfftacs])),step_case(ripple(direction_out,wave(direction_out,[1,1,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1],[zeroplus,imp(left)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,=>,[1],v1)]))then elementary(intro(new[y])then[intro(new[v2])then[elim(v2)then elim(v3)then[intro(right)then[hyp(v4),wfftacs],intro(right)then[hyp(v4),wfftacs]],wfftacs],wfftacs])))])]),lambda(x,p_ind(x,lambda(y,lambda(v0,inl(axiom))),[v0,v1,lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(lambda(v3,su(su(lambda(v4,su(v6,[v3 of su(v6,[v5 of v4],[v6])],[v6])),[v4 of v2],[v5]),[zeroplus of times(v0,v2)],[v4]))of(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,lambda(v3,su(lambda(v5,spread(v5,[v6,v7,inr(v7)])),[v1 of v2],[v4]))of(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(y,lambda(v2,spread(v2,[v3,v4,decide(v3,[v6,inr(v4)],[v7,inr(v4)])])))))),[term_of(zeroplus)],[zeroplus])),[v3 of v2],[v4]),[times2 of v0],[v3]),[term_of(times2)],[times2]))])),
[
]).
